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Finding the limit of a function in f(x)-f(a)/x-a format

  1. Oct 18, 2011 #1
    1. The problem statement, all variables and given/known data
    Let f(x)=lim (csct-cscx)/t-x. Find the value of f'(pi/4)
    t-x

    2. Relevant equations
    f(x)-f(a)/x-a

    3. The attempt at a solution

    I tried doing it from first principles but couldn't figure out how to get rid of h. I also tried doing L'hopital's rule and got root2 but I know the answer is 3root2. I also tried making the equation (cscx-root2)/x-(pi/4). Nothing seems to work!
     
  2. jcsd
  3. Oct 18, 2011 #2

    Mark44

    Staff: Mentor

    Use parentheses around the terms in the denominator.
    Use parentheses around the numerator and denominator terms.
    There is no h anywhere in your work.
    Assuming that f(x) = csc(x), then f'([itex]\pi/4[/itex]) is given by this limit.
    [tex]\lim_{x \to \pi/4}\frac{csc(x) - csc(\pi/4)}{x - \pi/4}[/tex]

    My first step was to rewrite the csc terms using csc(x) = 1/sin(x). After that, I did some algebra to write the whole limit expression with a single numerator and a single denominator. If you are allowed to use L'Hopital's Rule, you get the answer pretty quickly.
     
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